# Orthogonal functions

1. Oct 15, 2006

### stunner5000pt

In the first hald of this question it was proven that

$$-\frac{\hbar^2}{2m} \frac{d}{dx} \left[ \phi_{m}^* \frac{d \phi_{n}}{dx} - \phi_{n} \frac{d \phi_{m}^*}{dx}\right] = (E_{m} - E_{n}) \phi_{m}^* \phi_{n}$$

By integrating over x and by assuming taht Phi n and Phi m are zero are x = +/- infinity show that

$$\int_{-infty}^{infty} \phi_{m}^*(x) \phi_{n}(x) dx = 0$$ if Em is not En

so for this do i simply integrate that above expression wrt x?? is it really that simple?

2. Oct 15, 2006

### quasar987

I'd say so.

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